The reason you only have 1 pair in the hash, instead of 4 pairs, is that you keep initializing the hash inside the while loop:

        %animals_hash = (
            $animal => $sums,
        );
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Change that to:

    $animals_hash{$animal} = $sums;
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Here is a complete working example:

use warnings;
use strict;

my %animals_hash;
while (my $line = <DATA>) {
    chomp $line;
    my ( $sums, $animal ) = split /\s+/, $line;
    $animals_hash{$animal} = $sums;
}

use Data::Dumper;
$Data::Dumper::Sortkeys=1; 
print Dumper(\%animals_hash);

__DATA__
455 DOG
1074 BIRD
605 CAT
850 FISH
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Outputs:

$VAR1 = {
          'BIRD' => '1074',
          'CAT' => '605',
          'DOG' => '455',
          'FISH' => '850'
        };
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